Characterizations of regular local rings in positive characteristics

Author:
Jinjia Li

Journal:
Proc. Amer. Math. Soc. **136** (2008), 1553-1558

MSC (2000):
Primary 13A35, 13D07, 13D25, 13H05.

Published electronically:
November 23, 2007

MathSciNet review:
2373583

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Abstract | References | Similar Articles | Additional Information

Abstract: In this note, we provide several characterizations of regular local rings in positive characteristics, in terms of the Hilbert-Kunz multiplicity and its higher counterparts . We also apply the characterizations to improve a recent result by Bridgeland and Iyengar in the characteristic case. Our proof avoids using the existence of big Cohen-Macaulay modules, which is the major tool in the proof of Bridgeland and Iyengar.

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Additional Information

**Jinjia Li**

Affiliation:
Department of Mathematics, Syracuse University, 215 Carnegie, Syracuse, New York 13244

Email:
jli32@syr.edu

DOI:
https://doi.org/10.1090/S0002-9939-07-09158-7

Keywords:
Regular local ring,
Hilbert-Kunz multiplicity,
Frobenius,
Tor

Received by editor(s):
December 1, 2006

Received by editor(s) in revised form:
February 19, 2007

Published electronically:
November 23, 2007

Communicated by:
Bernd Ulrich

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.